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A257974 Prime numbers that are not the sum of one or more consecutive triangular numbers.

%I A257974 #37 Jan 19 2019 04:14:59
%S A257974 2,5,7,11,13,17,23,29,37,41,43,47,53,59,61,67,71,73,79,89,97,101,103,
%T A257974 107,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
%U A257974 211,223,227,229,233,239,241,257,263,269,271,277,281,283
%N A257974 Prime numbers that are not the sum of one or more consecutive triangular numbers.
%C A257974 Subsequence of primes of A050941. - _Michel Marcus_, Dec 14 2015
%C A257974 Prime numbers that are not the difference of two tetrahedral numbers (A000292). - _Franklin T. Adams-Watters_, Dec 16 2015
%H A257974 Chai Wah Wu, <a href="/A257974/b257974.txt">Table of n, a(n) for n = 1..10000</a>
%e A257974 From _Michael De Vlieger_, Nov 06 2015: (Start)
%e A257974 3 is a triangular number thus is not a term.
%e A257974 The triangular numbers <= 7 are {1, 3, 6}. None of these are 7. 7 is not found among the sums of adjacent pairs of terms, i.e., {{1, 3}, {3, 6}} = {4, 9}. The sum of all numbers {1, 3, 6} = 10. Thus 7 is a term.
%e A257974 The triangular numbers <= 19 are {1, 3, 6, 10, 15}. 19 is not a triangular number. 19 is not found among sums of pairs of adjacent terms {4, 9, 16, 25} nor among those of quartets of adjacent terms {20, 34}, but is found among sums of triples of adjacent terms {10, 19, 31}. Thus 19 is not a term. (End)
%p A257974 isA257974 := proc(n)
%p A257974     if isprime(n) then
%p A257974         return not isA034706(n) ;
%p A257974     else
%p A257974         false ;
%p A257974     end if;
%p A257974 end proc:
%p A257974 for n from 0 to 400 do
%p A257974     if isA257974(n) then
%p A257974         printf("%d,",n) ;
%p A257974     end if;
%p A257974 end do: # _R. J. Mathar_, Dec 14 2015
%t A257974 t = Array[Binomial[# + 1, 2] &, {10^4}]; fQ[n_] := Block[{s}, s = TakeWhile[t, # <= n &]; AnyTrue[Flatten[Total /@ Partition[s, #, 1] & /@ Range[Length@ s - 1]], # == n &]]; Select[Prime@ Range@ 120, ! fQ@ # &] (* _Michael De Vlieger_, Nov 06 2015, Version 10 *)
%Y A257974 Cf. A050941, A000217, A000292, A125602, A269414.
%K A257974 nonn
%O A257974 1,1
%A A257974 _Vicente Izquierdo Gomez_, Nov 05 2015
%E A257974 More terms from _Michael De Vlieger_, Nov 06 2015